Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16837132 |
| Sylow | C59 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479285, C4×#16837132, #28479295, … |
| maximal normal subgroup of | #28479285, C4×#16837132, #28479295, … |
| maximal quotient of | C2×#21421918, C2×#21421921, #28476637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2886);